Anomalous Exponent of the Spin Correlation Function of a Quantum Hall Edge

TL;DR

This paper investigates the spin and charge correlation functions in quantum Hall edge states, revealing an anomalous exponent in the spin correlation crossover due to Coulomb interactions, which can be experimentally measured.

Contribution

It introduces the concept of an anomalous exponent in the spin correlation function caused by Coulomb interactions in quantum Hall edges, using effective Hamiltonian and bosonization methods.

Findings

Crossover behavior differs for spin and charge correlations.

Anomalous exponent arises from long-wavelength effective interactions.

Nuclear spin relaxation rates can measure the anomalous exponent.

Abstract

The charge and spin correlation functions of partially spin-polarized edge electrons of a quantum Hall bar are studied using effective Hamiltonian and bosonization techniques. In the presence of the Coulomb interaction between the edges with opposite chirality we find a different crossover behavior in spin and charge correlation functions. The crossover of the spin correlation function in the Coulomb dominated regime is characterized by an anomalous exponent, which originates from the finite value of the effective interaction for the spin degree of freedom in the long wavelength limit. The anomalous exponent may be determined by measuring nuclear spin relaxation rates in a narrow quantum Hall bar or in a quantum wire in strong magnetic fields.